In “Nouvelle Vague,” Richard Linklater’s ingenious and enchanting docudrama about the making of “Breathless,” the 29-year-old Jean-Luc Godard (Guillaume Marbeck) never takes off his sunglasses. He wears them on the set and in the office, in restaurants and at the movies. (The film doesn’t have a bedroom scene, but if it did he might wear them there too.)

The omnipresent round dark shades serve several functions. First and foremost, they’re authentic — Godard, in the late ’50s and early ’60s, really did wear his sunglasses all the time, almost as a form of branding. They were instrumental in lending him his mystique: that of an intellectual artist who was cool, who knew how to keep his distance, who had things on his mind he was too hip to share. Yet the sunglasses also accomplish something else. In a biopic, no actor looks exactly like the person they’re playing. But the unknown French actor Guillaume Marbeck, with a bushy widow’s peak and a chiseled poker face, looks astoundingly like Godard, and without the eyes to give him away the resemblance is all but perfect. I was also amazed at how much Marbeck nails Godard’s voice — pensive and nasal in a musical way, with a hint of a reedy tremor in it.

Watching “Nouvelle Vague,” we don’t have to squint a bit to pretend that this is Jean-Luc Godard. It seems, rather, that Godard has sprung to life before us. And that uncanny quality extends to the entire movie, which plunks us down in Paris in 1959, in many of the same streets and boulevards and cafés and hotel rooms where “Breathless” was shot. The movie is in French with subtitles, and it uses lustrous high-contrast black-and-white cinematography (by David Chambille) to mirror the look of “Breathless,” and to make us feel like we’re right there, mingling with Godard and Truffaut and Chabrol and Jean-Paul Belmondo and Jean Seberg and Jean-Pierre Melville, as if we’d dropped in by time machine.

The first half hour of “Nouvelle Vague” introduces us to Godard and his colleagues on the French new wave scene, and it shows him maneuvering to direct his first movie, a privilege he thinks is long overdue, since he and his fellow critics at Cahiers du Cinéma have all vowed to become filmmakers. The owlish Chabrol has already made two features, and the debonair Truffaut has finished “The 400 Blows”; Godard, a thief when he needs to be, lifts money out of the Cahiers till to go to the Cannes Film Festival for “The 400 Blows” premiere. The film is received ecstatically, as everyone realizes they’re seeing the next generation of French cinema.

Now it’s Godard’s turn, if he can strike a deal with the producer Georges de Beauregard (Bruno Freyfürst). Godard does so by agreeing to make a gangster-and-a-girl movie based on a treatment by Truffaut, and by saying he’ll shoot it in 20 days. He recruits his young movie-actor acquaintance, the twisty-lipped hunk Jean-Paul Belmondo (Aubry Dullin), to play a small-time hoodlum antihero, and he approaches Jean Seberg (Zoey Deutch), an American movie star coming off the unhappy experience of working with Otto Preminger in “Bonjour Tristesse,” to play the American girl who gets involved with him. As far as the crew goes, it’s pretty simple: He recruits the tall and personable Raoul Coutard (Matthieu Penchinat) to be his cameraman, since Coutard shot documentary footage of the French Indochina War and Godard wants “Breathless” to look and feel like a documentary.

Godard has chosen to make “Breathless” in a particular way, and part of his slyness is that he’s going to do it without saying it out loud. Yes, the movie has locations and costumes, and yes, there’s a “script.” But Godard is seized by an insurrectionary idea: He’s basically going to make up “Breathless” as he goes along.

Once “Nouvelle Vague” arrives at the shooting of “Breathless,” the rest of the film is devoted to what happened during the shoot. And the reason this is elating to watch — in the way that a movie about the making of almost any other movie might not be — is that there’s barely any separation between the film Godard is making and what’s happening off camera.

“Nouvelle Vague” isn’t a comedy, yet there’s a deadpan comic dimension to it, and it has to do with what an insanely minimal process the making of “Breathless” was, and what it actually took for Godard to get away with that. On the first day of shooting, the first time he says “Action,” we think something is missing, because all we see is a casual handful of people standing on the street, with a small camera set up opposite a phone booth. There’s no lighting equipment (because the film is going to be made with natural light), and no sound (because it’s all going to be post-synced). I’ve seen students making a short for their college film class that looked like a bigger production than this.

Godard’s method is all about the inspiration of the moment, which means that he’ll do something like shoot for two hours and then take the rest of the day off. Each morning, at the Dupont Montparnasse, he scribbles down some version of what the actors are going to say that day, and feeds them the lines as they go along. It may sound like he’s inventing low-budget independent film. But here’s the reason he’s not.

In 1957, two years before Godard made “Breathless” (the movie premiered in January 1960), John Cassavetes shot his own first film, “Shadows,” which essentially did invent independent filmmaking as we know it. He did some of the same things Godard did. But “Shadows” was a work that broke completely with Hollywood. The glory of “Breathless” is that it’s a loose, semi-improvisatory extended bebop jazz solo of a movie, but it’s also rooted in the metaphysics of Hollywood: in movie stardom, in the tropes of gangsters and femme fatales, in the majesty of Bogart. Godard, in his genius literary screw-loose way, was making the stripped-to-the-sidewalls version of an old-fashioned movie, and that’s why the shooting of “Breathless” was, among other things, a fantastic balancing act.

He had to feed the ego of his stars, he had to convince Seberg — just about every day — that what she doing was not career suicide, and he had to convince his producer that what he was making was a real movie. Part of the charm of Godard in “Nouvelle Vague” is seeing what an ace schmoozer he is. He’ll do whatever it takes: jump rope with Belmondo, do a walking handstand. But his calling card is that he always needs to be the smartest person in the room, and he does it with such caustic wit that he has a way of leaving everyone around him in a pleasurable daze. (They don’t know what hit them.)    

He keeps having encounters with famous older directors, and that’s the one place where he’s deferential, because he seems to be friends with all of them: Roberto Rossellini (Laurent Mothe), who comes to the Cahiers du Cinema offices; Jean-Pierre Melville (Tom Novembre), who Godard recruits for a cameo in “Breathless”; or Robert Bresson (Aurélien Lorgnier), who he runs into when Bresson is shooting “Pickpocket” in the subway. These filmmakers give him tips, sharing their secrets, but what connects the advice is that they’re really inviting Godard into their private club of karmic explorers. They understand that the hidden nature of filmmaking is that it’s too big, too unwieldy, too unpredictable for a director to fully control the process. All he can do is guide it.

I think it’s that perception that makes “Nouvelle Vague” such a personal film for Linklater, and his most exquisite achievement since “Boyhood.” It’s clear how deeply he identifies with Jean-Luc Godard, who comes off here as a puckish and sly dictator. He speaks in epigrams (“You should never adapt a book to the cinema, you should adapt the cinema to a book,” “A filmmaker is either a plagiarist or a revolutionary”), and he does perverse things like insist that a cup stay in the shot even if it breaks continuity. At times, he and Coutard seem to be creating the very first motion picture — mounting the camera on a car for a makeshift tracking shot, or placing it inside a cart that Coutard crams himself into, so that it’s invisible and they can use the Paris pedestrians as unpaid extras. The ingenuity of “Breathless” was miraculous, and Linklater mirrors that ingenuity in the spontaneous bravura with which he re-creates it.

But “Nouvelle Vague” also has a great theme. There’s a driving concept behind Godard’s technique, and in many ways he’s open about it: toss off the dialogue, never do more than one or two takes, shoot when you feel like it and not just to meet the schedule, find the visual poetry in real locations. But what he’s keeping inside that wry egghead of his is the secret that will hold all of this together — that if it works, he’s going to capture the lightning of reality in a bottle, and that will revolutionize what cinema can be. Even the jump-cut that came to define “Breathless” happens for a logistical reason. They have far too much footage, so Godard tells his editors: Don’t cut any scenes — just cut each scene down to its highlights. (Spoken by someone who’s either a postmodern cinema visionary or an early case of ADHD, or both.)

Just about all the actors in “Nouvelle Vague” are lusciously right for their roles. Aubry Dullin makes Belmondo a sweet-souled rogue, and Zoey Deutch’s Seberg is a force. Linklater introduces each character by flashing his or her name on screen (there’s a lot of late-‘50s Paris cinema inside baseball), and though you wish you saw more of some of them (like Agnès Varda), it’s a savory pleasure to be able to step into this time machine and luxuriate in the company of people who thought that movies were the only thing that mattered. “Nouvelle Vague” is a Linklater gem, and arriving now it really is the right movie at the right time. In an age when blockbuster overkill is supposed to be saving movies, it reminds you that the real salvation of cinema will always come from those who understand that making a movie should be a magic trick good enough to fool the magician himself into believing it.